DESCRIPTION: The investigators associated with this project will develop new statistical and numerical tools for modeling dynamic social networks. These tools will address the needs of both applied and theoretical epidemiologists and social scientists studying the transmission of diseases and behaviors within partnerships. Potential applications include studies of HIV transmission through drug equipment and sex, and the dissemination of risk reduction through social contacts. The framework will use a dynamic version of Markov graphs to express the dependencies among partnerships. Monte Carlo Markov chains will be used for simulations. The tools that will be developed include software for sampling, hypothesis testing, and estimation. They will also include mathematical and statistical methods to predict the epidemiological impact of network structure and to adjust network studies to take into account sampling schemes. The tools will be applied to the analysis of networks of intravenous drug users and prostitutes in Brooklyn and Colorado Springs.